6.808: Mobile and Sensor Computing Lecture 8: Introduction to - - PowerPoint PPT Presentation

6.808: Mobile and Sensor Computing

Lecture 8: Introduction to Inertial Sensing & Sensor Fusion

Some material adapted from Gordon Wetzstein (Stanford) and Sam Madden (MIT)

Example Application: Inertial Navigation

GPS only GPS+INS

Key Idea #1: Integrate acceleration data over time to discover location (Inertial Sensing)

Inertial Sensing alone is not enough for accurate positioning

• Errors accumulate over time

Source: INS Face Off MEMS versus FOGs

Key Idea #2: Fuse Data from Multiple Sensors (Sensor Fusion)

Reference

INS-alone

• utputs

This Lecture

Key Idea #2: Fuse Data from Multiple Sensors (Sensor Fusion) Key Idea #1: Integrate acceleration data over time to discover location (Inertial Sensing)

Let’s understand inertial sensing in the context of VR

• Goal: track location and
• rientation of head or other

device

• Coordinates: Six degrees of

freedom:

• Cartesian frame of

reference (x,y,z)

• Rotations represented by

Euler angles (yaw, pitch roll)

Source: Oculus

What does an IMU consist of? (Inertial Measurement Unit)

• Gyroscope measures angular velocity ω in degrees/s
• Accelerometer measures linear acceleration a in m/s2
• Magnetometer measures magnetic field strength m in

μT (micro-Teslas). Why is it called IMU?

History of IMUs

• Earliest use of gyroscopes goes back to German

ballistic missiles (V-2 rocket) in WW2 for stability

• In the 1950s, MIT played a central role in the

development of IMUs (Instrumentation Lab)

Where are IMUs used today?

Rest of this Lecture

• Basic principles of operation of different IMU

sensors: accelerometer, gyroscope, magnetometer

• Understanding Sources of Errors
• Dead reckoning by fusing multiple sensors

How Accelerometers Work

How Accelerometers Work

What matters is the displacement

Newton’s Law

F = ma

Hooke’s Law

F = kx = > a = k m x k (spring constant)

Why not simply use displacement to measure displacement?

• How do we measure displacement?
• Most common approach is to use capacitance

and MEMS (Micro electro-mechanical systems)

Measuring Displacement

• How do we measure displacement?
• Most common approach is to use capacitance

and MEMS (Micro electro-mechanical systems)

Measuring Displacement

MEMS Accelerometer

Mass

MEMS Accelerometer

Mass

x + +

• C = ϵ Area

x

Capacitor

How Gyroscopes Work?

• Assume Vx
• Apply ω
• Experiences a

fictitious force F(ω, Vx) following right hand rule

The Coriolis Effect

The Coriolis Effect

How Gyroscopes Work?

• Assume Vx
• Apply ω
• Experiences a fictitious

force F(ω, Vx) following right hand rule

The Coriolis Effect

Can measure F in a similar fashion and use it to recover ω

How Magnetometers Work

• E.g., Compass
• Measure Earth’s magnetic field

Measure voltage across the plate

Rest of this Lecture

• Basic principles of operation of different IMU

sensors: accelerometer, gyroscope, magnetometer

• Understanding Sources of Errors
• Dead reckoning by fusing multiple sensors

Gyroscope

• How to get from angular velocity to angle?
• Integrate, knowing initial position

True angular velocity Measured angular velocity: Bias Noise (Gaussian, zero mean)

• Linear integration? What are we missing?

Gyro Integration

Angle (degrees) time (s)

• Let’s plot this for gyro

measurement and for

• rientation
• Let’s include ground truth

and measured data for each Consider:

• linear (angular) motion, no noise, no bias
• linear (angular) motion, with noise, no bias
• linear (angular) motion, no noise, bias
• nonlinear motion, no noise, no bias

Gyro integration: linear motion, no noise, no bias

Gyro measurement (angular velocity vs time) Actual orientation (angle vs time)

Gyro integration: linear motion, noise, no bias

Gyro measurement (angular velocity vs time) Actual orientation (angle vs time)

Gyro integration: linear motion, no noise, bias

Gyro measurement (angular velocity vs time) Actual orientation (angle vs time)

Gyro integration: nonlinear motion, no noise, no bias

Gyro measurement (angular velocity vs time) Actual orientation (angle vs time)

Gyro Integration aka Dead Reckoning

• Works well for linear motion, no noise, no bias = unrealistic
• Even if bias is known and noise is zero -> drift (from

integration)

• Bias and noise variance can be estimated, other sensor

measurements used to correct for drift (sensor fusion)

• Accurate in short term, but not reliable in long term due to

drift

Rest of this Lecture

• Basic principles of operation of different IMU

sensors: accelerometer, gyroscope, magnetometer

• Understanding Sources of Errors
• Dead reckoning by fusing multiple sensors

Dead Reckoning

• The process of calculating one's current position by

using a previously determined position, and advancing that position based upon known or estimated speeds

• ver elapsed time and course
• Key things to keep in mind:
• Frames of reference
• Orientation change

2D Inertial Navigation in Strapdown System

2D Inertial Navigation in Strapdown System

• Problems?

How about 3D Rotations?

Non-commutative = order matters!

3D Rotation Representations

• Rotation Matrix

– 3 orthonormal vectors = 9 numbers

• Euler Angles (roll, pitch, yaw)

– Symmetry problem, Gimbal lock

• Axis-angle
• Quaternions

– Hard to understand

Quaternions

• 4-dimensional number

Quaternions

https://youtu.be/zjMuIxRvygQ

ArmTrak (Tracking from Smart Watch)

Also fuse over time through hidden markov models (HMM)

Lecture Recap

• Importance of IMUs for navigation and sensing
• Coordinate systems and 6DOF
• IMU history and current use cases
• Basic principles of operation of different IMU sensors:

accelerometer, gyroscope, magnetometer

• Understanding Sources of Errors
• Dead reckoning by fusing multiple sensors